1. **State the problem:** Find the derivative of the function $f(x) = x^2$. 2. **Recall the power rule for derivatives:** If $f(x) = x^n$, then $f'(x) = nx^{n-1}$. 3. **Apply the power rule:** Here, $n=2$, so $$f'(x) = 2x^{2-1} = 2x.$$ 4. **Interpretation:** The derivative $2x$ gives the slope of the tangent line to the curve $y = x^2$ at any point $x$. **Final answer:** $$\frac{d}{dx} x^2 = 2x.$$